科研之友
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摘要
We consider the nonlinear Schrodinger equation with magnetic field and the Neumann boundary condition: @@@ {-del(2)(A)u + lambda u = vertical bar u vertical bar(p-2)u in Omega, @@@ nu . del(A)u = 0 on partial derivative Omega, @@@ where Omega is a boundary domain in R-n with a C-1 boundary, nu is the outward normal vector field at x epsilon partial derivative Omega, n >= 3, lambda > -mu(A), (mu(A) is given by (3)), A epsilon C-infinity((Omega) over bar, R-n) is a magnetic vector potential. Whenthe exponent is subcritical, 2 < p < 2* = 2n/n-2 wecan obtain solutions by Nehari manifold. When the exponent is critical, p = 2*, we can obtain solutions by constrained minimization arguments.
